Two products for which the demand schedules are related to each other
so that an increase in the price of the first good will cause a
leftward shift of the entire demand schedule for the other good(s) --
that is, less of the second good will now be demanded at any given
available price of the second good. (By the same token, a decrease in
the price of the first good will result in a rightward shift of the
entire demand schedule for the other good(s), so that more of the
second good will now be demanded at any given available price for the
second good.) This complementarity commonly happens when the
two goods tend to be consumed or used together in relatively fixed or
standardized proportions in at least some of their important
uses.

A classic example of complementary consumer goods would be
frankfurters and hot dog buns. If a supermarket runs a "special" on
hot dog buns, it is predictable that customers will want to buy more
frankfurters than they otherwise would at whatever is the posted price
of frankfurters -- because the total price of enjoying a frankfurter-
on-a-bun sandwich is now lower than before due to the special, leading
consumers to consume more of both component products.

A classic example of complementary producers' goods would be iron ore and
coking coal, the two main raw materials for making steel. If the price of
iron ore goes up, raising the steel companies' costs for making any given
amount of steel, ceteris paribus, they are apt
to cut back on the total quantity of steel they choose to produce. But if they
decide to produce less steel, they will now need to buy less coal -- and
therefore the amount of coal demanded at any given price of coal will be less
than before the iron ore price increase. (The same complementarity with iron
ore would also be evident with regard to all the other factors of production
besides coal that are used in making steel -- such as labor-hours of steel
workers, steel making machinery etc. The demand curve for each of them will
shift to the left in response to increases in the price of coal or any of
their other complementary goods or services.)